1. Field of the Invention
This invention relates generally to digital filters and, more particularly, to the implementation of sharp cut-off filters based on certain classes of functions used extensively in communication circuits. This invention relates to the digital implementation of infinite impulse response (IIR) filters and finite response (FIR) filters.
2. Description of the Related Art
Digital filters receive an sampled digital signal and transmit the sampled waveform therethrough. The waveform transmitted by the digital filter is determined by coefficients operating on portions of the transmitted digital signal. A digital filter, according to the prior, is shown in FIG. 1. The digital signal is applied to, and transmitted by, a series of delay components 11. Each delay component 11 applies an output signal to a coefficient multiplication component 12. The signal from each delay line is multiplied, in the coefficient multiplication component 12, by a weighing factor derived from a transform function. The output signal from the coefficient multiplication components 12 are applied to the output terminal and provide the output signal. Thus, an input signal applied to the digital filter is, after an appropriate time delay, filtered according to the coefficient multiplier components and the resulting signal is applied to the output terminal.
Sharp cut-off digital filters find extensive use in communication circuits and are used more generally to reduce aliasing, i.e., artifacts which can occur in transmitted images as a result of rapid image change. Root raised cosine function and sin(x)/x function are examples of transform functions which can provide the coefficients for sharp cut-off digital filters. Referring to FIG. 2, a sin(x)/x function is illustrated. This function can be used as a transform function for a digital filter when the coefficients for the coefficient multiplier components are chosen from the value of the sin(x)/x waveform at locations corresponding to the delay in time resulting from passage through the delay components, for example, at points along the axis. The center of the transform function is typically specified to occur at time t=0 or t.sub.0. The portions of the transform function to the left of the function center (t.sub.0) are referred to as the negative time portions and the portions of the transform function to the right of the function center (t.sub.0) are referred to as the negative time portions. Portions of the digital filter associated with the portions of the transform function can be similarly designated. The response of a digital filter to an impulse function typically exists for a long period of time. Therefore, FIR filters require a large number of delay components and associated coefficient multiplier components. The large number of delay elements required to implement a sharp cut-off digital filter presents problems in the design and fabrication of these devices.
A need has therefore been felt for apparatus and an associated method for providing a sharp cut-off digital filter which substantially reduces the number of delay lines and the associated coefficient multiplier components required to implement the related transform functions.